Ladder Operators for Lamé Spheroconal Harmonic Polynomials
| Autor: | R. Méndez-Fragoso, Eugenio Ley-Koo |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
spheroconal harmonics
Pure mathematics Angular momentum Quantum Physics lcsh:Mathematics Mathematical analysis Eigenfunction Quantum number lcsh:QA1-939 law.invention symbols.namesake ladder operators Ladder operator law symbols Cartesian coordinate system Geometry and Topology Angular momentum operator Hamiltonian (quantum mechanics) Analysis Mathematical Physics Lamé polynomials Mathematics Principal axis theorem |
| Zdroj: | Symmetry, Integrability and Geometry: Methods and Applications, Vol 8, p 074 (2012) |
| ISSN: | 1815-0659 |
| Popis: | Three sets of ladder operators in spheroconal coordinates and their respective actions on Lam\'e spheroconal harmonic polynomials are presented in this article. The polynomials are common eigenfunctions of the square of the angular momentum operator and of the asymmetry distribution Hamiltonian for the rotations of asymmetric molecules, in the body-fixed frame with principal axes. The first set of operators for Lam\'e polynomials of a given species and a fixed value of the square of the angular momentum raise and lower and lower and raise in complementary ways the quantum numbers $n_1$ and $n_2$ counting the respective nodal elliptical cones. The second set of operators consisting of the cartesian components $\hat L_x$, $\hat L_y$, $\hat L_z$ of the angular momentum connect pairs of the four species of polynomials of a chosen kind and angular momentum. The third set of operators, the cartesian components $\hat p_x$, $\hat p_y$, $\hat p_z$ of the linear momentum, connect pairs of the polynomials differing in one unit in their angular momentum and in their parities. Relationships among spheroconal harmonics at the levels of the three sets of operators are illustrated. |
| Databáze: | OpenAIRE |
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